Boyle's Law Formula

Boyle's law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely related.

The Formula

P1V1=P2V2P_1V_1 = P_2V_2

When to use: Squeeze a gas into less space and it pushes back harder.

Quick Example

If the volume of a gas is cut in half while temperature stays the same, the pressure doubles.

Notation

PP is pressure and VV is volume. At constant temperature and amount of gas, P1V1=P2V2P_1V_1 = P_2V_2 — pressure and volume are inversely proportional.

What This Formula Means

Boyle's law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely related.

Squeeze a gas into less space and it pushes back harder.

Worked Examples

Example 1

medium
A weather balloon at ground level holds 5 L5\text{ L} at 1 atm1\text{ atm}. At altitude (same TT) the volume is 20 L20\text{ L}. What is the pressure at altitude?

Answer

0.25 atm0.25\text{ atm}

First step

1
P2=P1V1/V2=1×5/20=0.25 atmP_2 = P_1 V_1 / V_2 = 1 \times 5 / 20 = 0.25\text{ atm}.

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Example 2

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A scuba tank holds 12 L12\text{ L} at 200 atm200\text{ atm}. At constant TT, what volume would that gas occupy at 1 atm1\text{ atm}?

Example 3

medium
P1=1.0 atmP_1 = 1.0\text{ atm}, V1=22.4 LV_1 = 22.4\text{ L}. At constant TT, what pressure forces the gas into 5.6 L5.6\text{ L}?

Common Mistakes

  • Using Boyle's law when temperature changes - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement.
  • Forgetting that pressure and volume change in opposite directions - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement.
  • Mixing pressure units without converting them first - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement. - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement.
  • Using boyle's law from a keyword alone - Signal words like gas, pressure, volume only point to a possible model; the substances and evidence must match too. - Fix this by naming the substances or sample, checking "Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant?", and attaching units, formulas, states, or evidence to the final statement.

Why This Formula Matters

Boyle's Law helps students reason about gases as particle systems rather than loose formulas. It connects lab measurements to molecular motion and conditions.

Frequently Asked Questions

What is the Boyle's Law formula?

Boyle's law states that for a fixed amount of gas at constant temperature, pressure and volume are inversely related.

How do you use the Boyle's Law formula?

Squeeze a gas into less space and it pushes back harder.

What do the symbols mean in the Boyle's Law formula?

PP is pressure and VV is volume. At constant temperature and amount of gas, P1V1=P2V2P_1V_1 = P_2V_2 — pressure and volume are inversely proportional.

Why is the Boyle's Law formula important in Chemistry?

Boyle's Law helps students reason about gases as particle systems rather than loose formulas. It connects lab measurements to molecular motion and conditions.

What do students get wrong about Boyle's Law?

Students often know a formula related to boyle's law but skip the recognition step: Am I comparing gas variables with units and temperature in kelvin, while holding the stated variables constant? That leads to a correct-looking substitution attached to the wrong chemical model.

What should I learn before the Boyle's Law formula?

Before studying the Boyle's Law formula, you should understand: gas laws.

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Related Concepts

Gas LawsCharles's Law